Combinatorial Matrix Theory

Judith J McDonald
Washington State University

Combinatorial matrix theory is the study of properties of a matrix that depend
on qualitative rather than quantitative information. The ideas developed are
important in many applications since they can provide reliable information about
a model even when the data is incomplete or inaccurate. The theory behind qualitative
methods can also contribute to the development of effective quantitative matrix
methods. We will look at some classical results in combinatorial matrix theory,
in particular the Perron-Frobenius theorem for nonnegative matrices. We will
discuss some recent extensions to reducible matrices and other classes, and
mention some areas where these ideas come up in economics, control theory and
numerical methods.